Polynomial vs. Non-Polynomial Functions Even vs. Odd Functions; End Behavior Read 4.1 Examples 1-3

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1 HW # Name Period Row Date Polynomial vs. Non-Polynomial Functions Even vs. Odd Functions; End Behavior Read.1 Eamples 1- Section.1. Which One Doesn't Belong? Which function does not belong with the other three? Eplain your reasoning. In Eercises 8, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. (See Eample 1.) 5 1. f ( ) = f ( ) = h ( ) = 9. Describe and correct the error in analyzing the function f ( ) = Evaluate the function for the given value of. (See Eample.) h ( ) = + 1 6; = In Eercises 17-0, describe the end behavior of the graph of the function. (See Eample.) h ( ) = f ( ) =

2 1. Describe the degree and leading coefficient of the polynomial function using the graph.. Using Structure Determine whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient ) ( = f Section.8 Determine whether the function is even, odd, or neither. (See Eample.) 1. ) ( + = f. 1 5 ) ( + + = g. 9 ) ( + = f

3 HW # Name Period Row Date Adding, Subtracting & Multiplying Polynomials Section.1 Analyzing Relationships In Eercises 6, describe the -values for which (a) f is increasing or decreasing, (b) f ( ) > 0, and (c) f ( ) < 0. Section. 5. Find the sum. (See Eample 1.) 5 (1 + 5) + ( ) In Eamples 9-1, find the difference. (See Eample.) 9. ( + 8) (5 + 1 ) ( ) (9 1 + ) 15. Modeling With Mathematics During a recent period of time, the numbers (in thousands) of males M and females F that attend degree-granting institutions in the United States can be modeled by M = 19.7t t F = 8t + 68t where t is time in years. Write a polynomial to model the total number of people attending degree-granting institutions. Interpret its constant term.

4 In Eercises 17, find the product. (See Eample.) ( ) 19. (5 + 6)( + ). ( 9 + 7)( + 1) 5. Error Analysis: Describe and correct the error in performing the operation. In Eercises 7, find the product of the binomials. (See Eample.) 7. ( )( + )( + )

5 HW # Name Period Row Date Factoring with GCF, Difference of Two Squares, By Grouping, & Trinomials (a=1) Read. / Eamples 1 & Section. In Eercises 5 1, factor the polynomial completely. (See Eample 1.) k 100k 7. 5 p 19 p m m + 6m 1. Error Analysis Describe and correct the error in factoring the polynomial. In Eercises 0, factor the polynomial completely. (See Eample.). 5 6 y y + y 0 5. a + 18a + 8a q 16q 9q + 6

6 HW #5 Name Period Row Date Factoring with Sum/Difference of Cubes, Quadratic Form, & Trinomials (a > 1) Read. / Eamples & Section. In Eercises 5 1, factor the polynomial completely. (See Eample 1.) q + 9q 18q w 19w + 6w 8 In Eercises 1 0, factor the polynomial completely. (See Eample.) g h 19h t + 50t In Eercises 1 8, factor the polynomial completely. (See Eample.) 1. 9k z 81. c + 9c r 8 + r 5 60r

7 HW #6 Name Period Row Date Dividing Polynomials Including Synthetic Division Read. Eamples 1- Section. Divide using polynomial long division. (See Eample 1.) 5. ( + 17) ( ) 7. ( ) ( 1) In Eercises 11 18, divide using synthetic division. (See Eamples and.) 11. ( ) ( ) 1. ( + 7) ( + 5) 15. ( + 9) ( ) 17. ( ) ( 6)

8 Error Analysis Describe and correct the error in using synthetic division to divide 5 + by. Maintaining Mathematical Proficiency Find the zero(s) of the function. (Sections.1 and.) 1. f ( ) = g ( ) =

9 HW #7 Name Period Row Date Section. 6. Divide using polynomial long division. (See Eample 1.) ( 1 5) ( 5) Remainder Theorem Read. Eample In Eercises 5, use synthetic division to evaluate the function for the indicated value of. (See Eample.) 5. f ( ) = 8 + 0; = 1 7. f ( ) = + + ; = 9. f ( ) = 6 + 1; = 6 1. f ( ) = ; =. Making an Argument You use synthetic division to divide f () by ( a) and find that the remainder equals 15. Your friend concludes that f ( 15) = a. Is your friend correct? Eplain your reasoning.

10 . Thought Provoking A polygon has an area represented by A = The figure has at least one dimension equal to +. Draw the figure and label its dimensions.

11 HW #8 Name Period Row Date The Factor Theorem Read. Eamples 5-7 Section. In Eercises 9, determine whether the binomial is a factor of the polynomial function. (See Eample 5.) 5 9. f ( ) = ; 1. h ( ) = ; + In Eercises 5 50, show that the binomial is a factor of the polynomial. Then factor the function completely. (See Eample 6.) 6. t ( ) = ; 5 7. f ( ) = ; 6 9. r ( ) = 7 + 8; + 7

12 Analyzing Relationships In Eercises 51 5, match the function with the correct graph. Eplain your reasoning. 51. f ( ) = ( )( )( + 1) 5. g ( ) = ( + )( + 1)( ) 5. h ( ) = ( + )( + )( 1) 5. k ( ) = ( )( 1)( + ) 69. Comparing Methods You are taking a test where calculators are not permitted. One question asks you to evaluate g(7) for the function g() = You use the Factor Theorem and synthetic division and your friend uses direct substitution. Whose method do you prefer? Eplain your reasoning. Maintaining Mathematical Proficiency Solve the quadratic equation by factoring. (Section.1) = 0 Solve the quadratic equation by completing the square. (Section.) = 0

13 HW # 9 Name Period Row Date Sketching Polynomial Functions Using Zeros and End Behavior Read.5 Eamples 1, and 5;.6 Eample 1 Section.5 In Eercises 1, solve the equation. (See Eample 1.). z z 1z = 0 9. c 6c = 1c 6c In Eercises 1 0, find the zeros of the function. Then sketch a graph of the function. (See Eample.) 1. h( ) = g ( ) = h ( ) = In Eercises 1 6, write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros. (See Eample 5.) 1.,, , 0, 5

14 Section.6 In Eercises 8, identify the number of solutions or zeros. (See Eample 1.) = 0 7. g ( s) = s s + s In Eercises 17 0, determine the number of imaginary zeros for the function with the given degree and graph. Eplain your reasoning. 17. Degree: 18. Degree: 5 0. Degree:

15 HW #0 Name Period Row Date Analyzing Graphs of Polynomial Functions Read.8 Eamples 1 and Section.8 1. Complete the Sentence A local maimum or local minimum of a polynomial function occurs at a point of the graph of the function.. Writing Eplain what a local maimum of a function is and how it may be different from the maimum value of the function. Analyzing Relationships In Eercises 6, match the function with its graph.. f ( ) = ( 1)( )( + ). h ( ) = ( + ) ( + 1) 5. g ( ) = ( + 1)( 1)( + ) 6. f ( ) = ( 1) ( + ) In Eercises 7 1, graph the function. (See Eample 1: Be sure to use this method, and not just graph it on your calculator!) 7. f ( ) = ( ) ( + 1) 9. h ( ) = ( + 1) ( 1)( ) Error Analysis Describe and correct the error in using factors to graph f. 15. f ( ) = ( + )( 1)

16 In Eercises 0, graph the function. Identify the -intercepts and the points where the local maimums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. (See Eample.). g ( ) = f ( ) = Open-Ended Sketch a graph of a polynomial function f having the given characteristics. The graph of f has -intercepts at =, = 0, and =. f has a local maimum value when = 1. f has a local minimum value when =. 7. Using Tools When a swimmer does the breaststroke, the function S = 1t t 1870t t 77t + 1t. t models the speed S (in meters per second) of the swimmer during one complete stroke, where t is the number of seconds since the start of the stroke and 0 t 1.. Use a graphing calculator to graph the function. At what time during the stroke is the swimmer traveling the fastest?

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